Known pneumatic tube installations of the type to which the invention relates generally are constructed in such a way that the sample despatch station is set up at and connected to the sampling facility (with sampler, sample mixer and metering unit) of a production plant, while the sample receiving station is set up at the sample processing facility, usually in a laboratory. The sample despatch station and the sample receiving station are connected to one another for delivery on the one hand by a vacuum delivery line and on the other hand by a compressed air delivery line, an air blower being associated with each of these two delivery lines. It is of course also possible for several sample despatch stations (distributed throughout the production plant) to be connected to the sample receiving station in the same way. Major disadvantages of this known construction include the fact that the expense which it involves in terms of delivery lines and the energy required for operating them is considerable, and the fact that both the sample despatch station and also the sample receiving station have to be connected to both delivery lines to ensure, on the one hand, the delivery of full sample carriers and, on the other hand, the return of empty sample carriers to the corresponding sample despatch station.